Let A=[a 1, a2, a3], and the determinant value of A will be non-zero, or A will make a row elementary transformation to get rank r(A)=3, then the equation group AX=0 has only zero solution. According to the definition of X 1A 1X2A2+X3A3 = 0, X65438. The landlord can write down the above three sentences and the proposition to be proved. One * * * four sentences are equivalent, and they can be proved to each other later. That is, matrix full rank = determinant is not zero = matrix column vector is linearly independent = matrix is linearly independent.